Problem: What number could replace $z$ below? $\dfrac{3}{4} = \dfrac{z}{12}$
Explanation: The fraction on the left represents 3 out of 4 slices of a rectangular cake. What if we cut the cake into 12 slices instead? How many slices would result in the same amount of cake? We would need 9 slices. $\dfrac{3}{4} = \dfrac{9}{12}$ and so the answer is $9$ Another way to get the answer is to multiply by $\dfrac{3}{3}$ $\dfrac{3}{3} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{3}{4} \times \dfrac{3}{3} = \dfrac{9}{12} $ so our answer is $9$.